Related papers: Multi-dimensional chaos I: Classical and quantum m…
Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…
The scattering matrix S of a ballistic chaotic cavity is the direct sum of a `classical' and a `quantum' part, which describe the scattering of channels with typical dwell time smaller and larger than the Ehrenfest time, respectively.…
We have identified ultra-cold atoms in magneto-optical double-well potentials as a very clean setting in which to study the quantum and classical dynamics of a nonlinear system with multiple degrees of freedom. In this system, entanglement…
The wave propagation in random medium plays a critical role in optics and quantum physics. Multiple scattering of coherent wave in a random medium determines the transport procedure. Brownian motions of the scatterers perturb each…
In recent years, analysis and control of quantum chaos are increasingly important, but the lack of the concept of trajectory makes it impossible to analyze quantum chaos by the methods used in classical chaos. This research aims to connect…
The classical dynamics and the construction of quantum states in a plane wave curved spacetime are examined, paying particular attention to the similarities with the case of an electromagnetic plane wave in flat spacetime. A natural map…
While classical chaos has been successfully characterized with consistent theories and intuitive techniques, such as with the use of Lyapunov exponents, quantum chaos is still poorly understood, as well as its relation with multi-partite…
Theoretical foundations of chaos have have been predominantly laid out for finite-dimensional dynamical systems, such as the three-body problem in classical mechanics and the Lorenz model in dissipative systems. In contrast, many real-world…
The quantum three-rotor problem concerns the dynamics of 3 equally massive particles moving on a circle subject to pairwise attractive cosine potentials and can model coupled Josephson junctions. Classically, it displays order-chaos-order…
Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting…
A widely accepted definition of ``quantum chaos'' is ``the behavior of a quantum system whose \emph{classical} \emph{limit is chaotic}''. The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical…
A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and…
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…
We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of "quantum chaotic dynamics". It is shown that under quite general conditions their roots…
We study quantum chaos in a non-KAM system, i.e. a kicked particle in a one-dimensional infinite square potential well. Within the perturbative regime the classical phase space displays stochastic web structures, and the diffusion…
Chaos is an important characterization of classical dynamical systems. How is chaos linked to the long-time dynamics of collective modes across phases and phase transitions? We address this by studying chaos across Ising and…
The spreading of entanglement in out-of-equilibrium quantum systems is currently at the centre of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
For chaotic scattering on quantum graphs, the semiclassical approximation is exact. We use this fact and employ supersymmetry, the colour-flavour transformation, and the saddle-point approximation to calculate the exact expression for the…
The relation between classically chaotic dynamics and quantum localization is studied in a system that violates the assumptions of Kolmogorov-Arnold-Moser (KAM) theorem, namely, kicked rotor in a discontinuous potential barrier. We show…